A Parallel Iterative hybrid Gauss–Jacobi–Seidel method

Abstract

In this paper, we introduce a new iterative hybrid method to find the solution of linear algebraic systems based on the Gauss–Jacobi and Gauss–Seidel methods, named Jacobi–Seidel Parallel Iterative Method, JASPIoM for short. This method shows a iteration matrix that allows to parallelize the processing and can be utilized in serial or parallel architectures. The mathematical formulation is presented and the tests are performed in parallel ambiance and its performance is evaluated, considering the time of execution, in comparison to the serial and parallelized Gauss–Jacobi method and serial Gauss–Seidel method. The computational experiment aimed at focusing on the differences in performance, considering the speedup of execution in serial and parallel context. The results show that the JASPIoM method presents good performance, indicating the efficiency and potential of this scheme.